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Fluorescein is perhaps the most commonly used substance to visualize tear film thickness and dynamics; better understanding of this process aids understanding of dry eye syndrome which afflicts millions of people. We study a mathematical…
We propose a particle-based method to simulate thin-film fluid that jointly facilitates aggressive surface deformation and vigorous tangential flows. We build our dynamics model from the surface tension driven Navier-Stokes equation with…
We study theoretically and experimentally how a thin layer of liquid flows along a flexible beam. The flow is modelled using lubrication theory and the substrate is modelled as an elastica which deforms according to the Euler-Bernoulli…
In this paper, we present a new model to simulate the formation, evolution, and break up of a thin film of fluid flowing over a curved surface. Referred to as the discrete droplet method (DDM), the model captures the evolution of thin fluid…
We present a method to simulate fluid flow on evolving surfaces, e.g., an oil film on a water surface. Given an animated surface (e.g., extracted from a particle-based fluid simulation) in three-dimensional space, we add a second simulation…
We consider the spreading of a thin two-dimensional droplet on a solid substrate. We use a model for viscous fluids where the evolution is governed by Darcy's Law. At the triple point where air and liquid meet the solid substrate, the…
Simulations of nematic-isotropic transition of liquid crystals in two dimensions are performed using an O(2) vector model characterised by non linear nearest neighbour spin interaction governed by the fourth Legendre polynomial $P\_4$. The…
The deformation of an elastic micro-capsule in an infinite shear flow is studied numerically using a spectral method. The shape of the capsule and the hydrodynamic flow field are expanded into smooth basis functions. Analytic expressions…
The goal of this paper is to propose two nonlinear variational models for obtaining a refined motion estimation from an image sequence. Both the proposed models can be considered as a part of a generalized framework for an accurate…
Flow through porous, elastically deforming media is present in a variety of natural contexts ranging from large-scale geophysics to cellular biology. In the case of incompressible constituents, the porefluid pressure acts as a Lagrange…
Dry Eye Disease (DED) is one of the most common ocular diseases: over five percent of US adults suffer from DED. Tear film instability is a known factor for DED, and is thought to be regulated in large part by the thin lipid layer that…
Dense flow visualization is a popular visualization paradigm. Traditionally, the various models and methods in this area use a continuous formulation, resting upon the solid foundation of functional analysis. In this work, we examine a…
The tear film (TF) plays a critical role in maintaining ocular surface health, and its disruption through tear breakup (TBU) is closely associated with dry eye disease. Evaporation-driven thinning is a primary mechanism underlying TBU, yet…
Deep learning has revolutionized the field of computer vision by introducing large scale neural networks with millions of parameters. Training these networks requires massive datasets and leads to intransparent models that can fail to…
In this work we consider optical flow on evolving Riemannian 2-manifolds which can be parametrised from the 2-sphere. Our main motivation is to estimate cell motion in time-lapse volumetric microscopy images depicting fluorescently labelled…
We extend the concept of optical flow with spatiotemporal regularisation to a dynamic non-Euclidean setting. Optical flow is traditionally computed from a sequence of flat images. The purpose of this paper is to introduce variational motion…
We study the one-dimensional capillary-driven retraction of a finite, planar liquid sheet in the asymptotic regime where both the Ohnesorge number $\mathrm{Oh}$ and the initial length-to-thickness ratio $l_0/h_0$ are large. In this regime,…
We consider a third order non-autonomous ODE that arises as a model of fluid accumulation in a two dimensional thin-film flow driven by surface tension and gravity. With the appropriate matching conditions, the equation describes the inner…
Many biological examples of fluid-structure interaction, including the transit of red blood cells through the narrow slits in the spleen and the intracellular trafficking of vesicles into dendritic spines, involve the near-contact of…
We propose a generic model for thin films and shallow drops of a polar active liquid that have a free surface and are in contact with a solid substrate. The model couples evolution equations for the film height and the local polarization…